Journal of the Franklin Institute, Volume 252Pergamon Press, 1951 Vols. 1-69 include more or less complete patent reports of the U. S. Patent Office for years 1825-1859. cf. Index to v. 1-120 of the Journal, p. [415] |
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Page 43
... equation , 720 = 0 ( b ) Poisson's equation , known function of the 720 coordinates , or a constant = - K ( u1 , u2 , u3 ) , where ... Helmholtz equation 43 Solutions of Some Partial Differential Equations (with Tables) LOUIS WEINBERG.
... equation , 720 = 0 ( b ) Poisson's equation , known function of the 720 coordinates , or a constant = - K ( u1 , u2 , u3 ) , where ... Helmholtz equation 43 Solutions of Some Partial Differential Equations (with Tables) LOUIS WEINBERG.
Page 44
... Helmholtz equation will be demonstrated . 3. Tables of solutions for eight of the most commonly used coordi- nate systems will be given . THE HELMHOLTZ EQUATION Consider the equations listed in the first paragraph : ( a ) It is evident ...
... Helmholtz equation will be demonstrated . 3. Tables of solutions for eight of the most commonly used coordi- nate systems will be given . THE HELMHOLTZ EQUATION Consider the equations listed in the first paragraph : ( a ) It is evident ...
Page 47
... equation is again the Helmholtz equation . ( 31 ) ( e ) When the above procedure is used on the damped - wave equation the separated time equation is d2T dT + Rc2 + y2c2T = 0 . dt2 dt The solution of the above gives where and α = T Rc2 ...
... equation is again the Helmholtz equation . ( 31 ) ( e ) When the above procedure is used on the damped - wave equation the separated time equation is d2T dT + Rc2 + y2c2T = 0 . dt2 dt The solution of the above gives where and α = T Rc2 ...
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